928:
1131:
two categories. In the first category, the MM region is polarized by the QM electric field but then does not act back on the QM system. In the second category are fully self-consistent formulations which allow for mutual polarization between the QM and the MM systems. polarized embedding schemes have scarcely been applied to bio-molecular simulations and have essentially been restricted to explicit solvation models where the solute will be treated as a QM system and the solvent a polarizable force field.
1118:. This means that polarization of the QM system by the electrostatic interactions with the MM system will now be accounted for. Though an improvement on the mechanical embedding scheme it comes at the cost of increased complexity hence requiring more computational effort. Another issue is it neglects the effects of the QM system on the MM system whereas in reality both systems would polarize each other until an equilibrium is met.
1140:
both affect the results and the time computing the results. The way the QM and MM systems are coupled can differ substantially depending on the arrangement of particles in the system and their deviations from equilibrium positions in time. Usually, limits are set at carbon-carbon bonds and avoided in regions that are associated with charged groups, since such an electronically variant limit can influence the quality of the model.
321:
1105:
is the site of the reaction thus it is likely that during the course of the reaction the charge distribution will change resulting in a high level of error if a single set of MM electrostatic parameters is used to describe it. Another problem is the fact that mechanical embedding will not consider the effects of electrostatic interactions with the MM system on the electronic structure of the QM system.
1158:
issue relates to polarisation, more specifically for electrostatic or polarized embedding it is important to ensure that the proximity of the MM charges near the boundary does not cause over-polarisation of the QM density. The final issue is the bonding MM terms must be carefully selected in order to prevent double counting of interactions when looking at bonds across the boundary.
923:{\displaystyle {\begin{aligned}E(QM/MM)&=\sum _{I'=1}^{MM}\left\\&+\sum _{\text{non-bonded pairs}}\left({\frac {A_{II'}}{R_{II'}^{12}}}-{\frac {B_{II'}}{R_{II'}^{6}}}\right)+\sum _{\text{bonds}}k_{r}(R_{II'}-r_{0})^{2}\\&+\sum _{\text{angles}}k_{\theta }(\theta -\theta _{0})^{2}+\sum _{\text{torsions}}\sum _{n}k_{\phi ,n}\end{aligned}}}
1083:. The MM charges that lie within the second sphere (but not the first) interact with the QM region by giving the QM nuclei constructed charges. These charges are determined by the RESP approach in an attempt to mimic electron density. Using this approach the changing charges on the QM nuclei during the course of a simulation are accounted for.
1202:
BuRNN (Buffer Region Neural
Network) approach was developed as an alternative to QM/MM methods. Its focus is to reduce artifacts that are created in between QM and MM region by introducing buffer region between them. Buffer region experiences full electronic polarization by the QM region and together
1181:
In boundary atom schemes, the MM atom which is bonded across the boundary to a QM atom is replaced with a special boundary atom which appears in both the QM and the MM calculation. In the MM calculation, it simply behaves as an MM atom but in the QM system it mimics the electronic character of the MM
1139:
Even though QM/MM methods are often very efficient, they are still rather tricky to handle. A researcher has to limit the regions (atomic sites) which are simulated by QM, however methods have been developed that allow particles to move between the QM and MM region. Moving the limitation borders can
1148:
Directly connected atoms, where one is described by QM and the other by MM are referred to as
Junction atoms. Having the boundary between the QM region and MM region pass through a covalent bond may prove problematic however this is sometimes unavoidable. When it does occur it is important that the
1130:
Whereas electrostatic embedding accounts for the polarisation of the QM system by the MM system, neglecting the polarization of the MM system by the QM system, polarized embedding accounts for both the polarization of the MM system by the QM. These models allow for flexible MM charges and fall into
1104:
Mechanical embedding treats the electrostatic interactions at the MM level, though simpler than the other methods, certain issues may occur, in part due to the extra difficulty in assigning appropriate MM properties such as atom centered point charges to the QM region. The QM region being simulated
1086:
In the third outermost region the classical charges interact with the multipole moments of the quantum charge distribution. By calculating charge-charge interactions by using successively more approximate methods it is possible to obtain a very significant reduction in computational cost whilst not
1157:
In systems where the QM/MM boundary cuts a bond three issues must be dealt with. First, the dangling bond of the QM system must be capped, this is because it is undesirable to truncate the QM system (treating the bond as if it has been cleaved will yield very unrealistic calculations). The second
139:
rather than the number of atoms. Each atom has at least as many basis functions as is the number of electrons. To overcome the limitation, a small part of the system that is of major interest is treated quantum-mechanically (for instance, the active site of an enzyme) and the remaining system is
1034:
Evaluating the charge-charge term in the QM/MM interaction equation given previously can be very computationally expensive (consider the number of evaluations required a system with 10 grid points for the electron density of the QM system and 10 MM atoms). A method by which this issue can be
1121:
In order to construct the required one electron terms for the MM region it is possible to utilize the partial charges described by the MM calculation. This is the most popular method for constructing the QM Hamiltonian however it may not be suitable for all systems.
148:
The energy of the combined system may be calculated in two different ways. The simplest is referred to as the 'subtractive scheme' which was proposed by
Maseras and Morokuma in 1995. In the subtractive scheme the energy of the entire system is calculated using a
1203:
with QM region is described by NN (neural network) trained on QM calculations. The substitution of QM calculations for NN also speeds up overall simulation. BuRNN was introduced in the 2022 paper of Lier, Poliak, Marquetand, Westermayr, and
Oostenbrink.
986:-stretching potentials that cross the boundary are accounted for by the fourth term. The final two terms account for the energy across the boundary that arises from bending covalent bonds and torsional potentials. At least one of the atoms in the angles
82:
is the number of atoms in the system. This is mainly due to electrostatic interactions term (every particle interacts with everything else). However, use of cutoff radius, periodic pair-list updates and more recently the variations of the
1095:
Electrostatic interactions between the QM and MM region may be considered at different levels of sophistication. These methods can be classified as either mechanical embedding, electrostatic embedding or polarized embedding.
1113:
Electrostatic embedding does not require the MM electrostatic parameters for the QM. This is due to it considering the effects of the electrostatic interactions by including certain one electron terms in the QM regions
1039:
spheres around the QM region and evaluate which one of these spheres the MM atoms lie within. If the MM atoms reside within the innermost sphere their interactions with the QM system are treated as per the equation for
977:
labels the MM nuclei. The first two terms represent the interaction between the total charge density (due to electrons and cores) in the QM region and classical charges of the MM region. The third term accounts for
269:
326:
1218:
315:
would refer to the energy of the QM region as calculated using molecular mechanics. In this scheme, the interaction between the two regions will only be considered at a MM level of theory.
1161:
Overall the goal is to obtain a good description of QM-MM interactions at the boundary between the QM and the MM system and there are three schemes by which this can be achieved.
1370:
Morzan UN, Alonso de Armiño DJ, Foglia NO, RamĂrez F, González
Lebrero MC, Scherlis DA, et al. (April 2018). "Spectroscopy in Complex Environments from QM-MM Simulations".
1243:
Warshel A, Levitt M (May 1976). "Theoretical studies of enzymic reactions: dielectric, electrostatic and steric stabilization of the carbonium ion in the reaction of lysozyme".
103:). In other words, if a system with twice as many atoms is simulated then it would take between twice to four times as much computing power. On the other hand, the simplest
42:(accuracy) and MM (speed) approaches, thus allowing for the study of chemical processes in solution and in proteins. The QM/MM approach was introduced in the 1976 paper of
1223:
313:
1081:
1004:
975:
1024:
950:
66:
An important advantage of QM/MM methods is their efficiency. The cost of doing classical molecular mechanics (MM) simulations in the most straightforward case
1333:"Mixed Quantum Mechanical/Molecular Mechanical Molecular Dynamics Simulations of Biological Systems in Ground and Electronically Excited States"
36:
1427:
1173:
to the atom being described by quantum mechanics which serves to saturate its valency (by replacing the bond that has been broken).
1169:
Link atom schemes introduce an additional atomic centre (usually a hydrogen atom). This atom is not part of the real system. It is
156:, then the energy of the QM system is added (calculated using a QM method), finally the MM energy of the QM system is subtracted.
1619:
1304:
1115:
318:
In practice, a more widely used approach is a more accurate, additive method. The equation for this consists of three terms:
161:
47:
1566:"BuRNN: Buffer Region Neural Network Approach for Polarizable-Embedding Neural Network/Molecular Mechanics Simulations"
1481:
Kerdcharoen T, Liedl KR, Rode BM (1996). "A QM/MM simulation method applied to the solution of Li+ in liquid ammonia".
1624:
55:
116:
1278:
979:
153:
1194:
at the boundary and keep some of them frozen. These orbitals cap the QM region and replace the cut bond.
1191:
136:
1490:
1149:
bond of the QM atom be capped in order to prevent the appearance of bond cleavage in the QM system.
150:
84:
28:
1036:
276:
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1397:
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24:
989:
1585:
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1387:
1379:
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1009:
1494:
955:
1590:
1565:
1309:
935:
67:
51:
1613:
1502:
1256:
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983:
43:
1581:
1383:
1466:
1449:
32:
1599:
1550:
1542:
1401:
1356:
1332:
1450:"QM/MM: what have we learned, where are we, and where do we go from here?"
1215:: "our own n-layered integrated molecular orbital and molecular mechanics"
1264:
58:
for "the development of multiscale models for complex chemical systems".
1564:
Lier B, Poliak P, Marquetand P, Westermayr J, Oostenbrink C (May 2022).
1392:
1348:
1529:
Senn HM, Thiel W (2009). "QM/MM methods for biomolecular systems".
1284:(Press release). Royal Swedish Academy of Sciences. October 9, 2013
1212:
1030:
Reducing the computational cost of calculating QM-MM interactions
1219:
List of quantum chemistry and solid state physics software
1046:
1012:
992:
958:
938:
324:
279:
264:{\displaystyle E=E^{QM}(QM)+E^{MM}(QM+MM)-E^{MM}(QM)}
164:
1075:
1026:will be a QM atom with the others being MM atoms.
1018:
998:
969:
944:
922:
307:
263:
1422:(2nd ed.). Oxford: Oxford University Press.
1224:List of software for molecular mechanics modeling
1182:atom bounded across the boundary to the QM atom.
144:Calculating the energy of the combined system
8:
1413:
1411:
1305:"3 Researchers Win Nobel Prize in Chemistry"
1524:
1522:
1520:
1518:
1516:
1514:
1512:
952:labels the nuclei in the QM region whereas
1443:
1441:
1439:
1087:suffering a significant loss in accuracy.
1589:
1570:The Journal of Physical Chemistry Letters
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163:
87:(PME) method has reduced this to between
1144:Covalent bonds across the QM-MM boundary
1235:
1418:Allen MP, Tildesley DJ (August 2017).
1331:Brunk E, Rothlisberger U (June 2015).
35:method that combines the strengths of
7:
1448:Lin H, Truhlar DG (February 2007).
1279:"The Nobel Prize in Chemistry 2013"
1091:The electrostatic QM-MM interaction
399:
14:
1035:mitigated is to construct three
563:
543:
469:
450:
435:
406:
982:across the QM/MM boundary. Any
107:calculations formally scale as
1454:Theoretical Chemistry Accounts
1420:Computer Simulation of Liquids
1070:
1050:
913:
904:
882:
873:
825:
805:
766:
731:
439:
431:
352:
332:
302:
293:
258:
249:
230:
212:
193:
184:
119:have been suggested to scale ~
1:
1503:10.1016/0301-0104(96)00152-8
1257:10.1016/0022-2836(76)90311-9
1245:Journal of Molecular Biology
1135:Problems involved with QM/MM
1582:10.1021/acs.jpclett.2c00654
1384:10.1021/acs.chemrev.8b00026
1303:Chang K (October 9, 2013).
16:Molecular simulation method
1641:
308:{\displaystyle E^{MM}(QM)}
31:) approach is a molecular
1467:10.1007/s00214-006-0143-z
1186:Localized-orbital schemes
135:stands for the number of
117:Hartree–Fock calculations
1076:{\displaystyle E(QM/MM)}
56:Nobel Prize in Chemistry
1620:Computational chemistry
999:{\displaystyle \theta }
980:dispersion interactions
115:) or worse (restricted
1543:10.1002/anie.200802019
1077:
1020:
1000:
971:
946:
924:
506:
390:
309:
265:
1177:Boundary atom schemes
1078:
1021:
1019:{\displaystyle \phi }
1001:
972:
947:
925:
483:
362:
310:
266:
140:treated classically.
1190:These schemes place
1109:Electronic embedding
1100:Mechanical embedding
1044:
1010:
990:
956:
936:
322:
277:
162:
50:. They, along with
1495:1996CP....211..313K
1126:Polarized embedding
700:
652:
151:molecular mechanics
85:particle mesh Ewald
29:molecular mechanics
1625:Molecular dynamics
1073:
1016:
996:
970:{\displaystyle I'}
967:
942:
920:
918:
856:
846:
794:
720:
678:
630:
604:
305:
261:
1576:(17): 3812–3818.
1531:Angewandte Chemie
1349:10.1021/cr500628b
1171:covalently bonded
1165:Link atom schemes
945:{\displaystyle I}
847:
844:
837:
792:
785:
718:
711:
701:
653:
602:
595:
578:
478:
273:In this equation
25:quantum mechanics
1632:
1604:
1603:
1593:
1561:
1555:
1554:
1526:
1507:
1506:
1483:Chemical Physics
1478:
1472:
1471:
1469:
1445:
1434:
1433:
1415:
1406:
1405:
1395:
1378:(7): 4071–4113.
1372:Chemical Reviews
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1361:
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1337:Chemical Reviews
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1322:
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1319:
1317:
1300:
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1153:Boundary schemes
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601:non-bonded pairs
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127:)). Here in the
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1537:(7): 1198–229.
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1343:(12): 6217–63.
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1192:hybrid orbitals
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137:basis functions
64:
54:, won the 2013
40:QM calculations
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1489:(1): 313–323.
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1310:New York Times
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131:calculations,
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52:Martin Karplus
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1251:(2): 227–49.
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984:covalent bond
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1116:Hamiltonian
154:force field
19:The hybrid
1614:Categories
1316:October 9,
1288:October 9,
1230:References
1037:concentric
932:The index
62:Efficiency
33:simulation
1014:ϕ
994:θ
896:δ
889:ϕ
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849:∑
839:∑
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129:ab initio
105:ab initio
78:), where
38:ab initio
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1207:See also
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68:scales
48:Levitt
1282:(PDF)
1213:ONIOM
1198:BuRNN
717:bonds
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21:QM/MM
1596:PMID
1547:PMID
1424:ISBN
1398:PMID
1353:PMID
1318:2013
1290:2013
1261:PMID
46:and
1586:PMC
1578:doi
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1388:hdl
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